The central focus of this article is on NLSE with LC and BLG terms for which, in addition to real-valued linear
and nonlinear couplings, the components of NLSE are subjected to loss or gain such that the power or a modified
form of it named as pseudo-power is conserved[1]}. The NLSE with balanced loss and gain
has been investigated over the last one decade or so and is known to admit bright[2]}, [3]} and dark solitons [4]}, breathers[5]},
rogue waves[6]}, exceptional points[5]}, [8]}, etc. Further, the power oscillation is observed in some specific
models which may have interesting technological applications[9]}. The NLSE with time-modulated loss-gain terms
have also been investigated numerically and shown its efficiency in the stabilization of solitons and soliton
switching[10]}, [11]}, [8]}. The NLSE with LC and BLG has also been investigated from the viewpoint of exact solvability and
exact analytical solutions of some models are constructed under specific reduction of the original equation[3]}, [14]}.
Recently, a method was prescribed to construct exactly solvable models of NLSE with LC and BLG by using a
non-unitary transformation which removes the LC and BLG terms completely at the cost of modifying the strength
of the nonlinear term[9]}. Further, the LC and BLG terms are removed completely without modifying the nonlinear
term at all for some specific models for which the non-unitary transformation can be identified as a
pseudo-unitary transformation. The method has been used to construct exactly solvable models exhibiting
power-oscillation.
